Two dimensional range minimum queries and Fibonacci lattices

Gerth Stølting Brodal,Pooya Davoodi,Moshe Lewenstein,Rajeev Raman,Srinivasa Rao Satti

doi:10.1016/j.tcs.2016.02.016

Two dimensional range minimum queries and Fibonacci lattices

Gerth Stølting Brodal, Pooya Davoodi + Show 3 more

Open Access

https://doi.org/10.1016/j.tcs.2016.02.016

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Journal: Theoretical Computer Science	Publication Date: Feb 17, 2016
License type: cc-by-nc-nd

Affiliation: Center for Massive Data Algorithmics, New York University, Bar-Ilan University, University of Leicester, Seoul National University

#Query Time #Indexing Data Structure + Show 8 more

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Abstract

Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique—the discrepancy properties of Fibonacci lattices—we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clog⁡c(log⁡log⁡c)2) query time, for any parameter c, 4≤c≤N. Also, when the entries of the input matrix are from {0,1}, we show that the query time can be improved to O(clog⁡c) with the same space usage.

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